Speaker
Description
We classify multi-partite entanglement measures and count them for large dimensional quantum systems. We compute these measures for two dimensional conformal field theories using twist operators and find that they are given by the lightest Virasoro conformal block in appropriate channel. In the limit of large central charge $c$, these blocks reduce to geodesic networks on the hyperbolic spatial slice of the dual bulk theory. For a general multi-partite entanglement measures the geodesics involved are generically heavy i.e. of tension $\mathcal{O}(c)$ and backreact on the geometry. We find a special any-partite measure, dubbed multi-entropy, that has the following desirable properties: 1) It is symmetric with respect to all the parties involved. 2) For two parties, it reduces to the von Neumann entropy. 3) The geodesics describing its holographic dual are light probes of the background geometry. The holographic dual of multi-entropy has a natural extension to account for the quantum excitations in the bulk and admits an elegant generalization to higher dimensions as ``minimal area soap-film". We also describe how previously known measures of multi-partite entropies such as reflected entropy fit naturally in our framework. We believe that this is the beginning of a program that will be useful to shed light on entanglement structure of the holographic duality, in particular on encoding of the gravitational Hilbert space in the conformal field theory Hilbert space.
